声学四极子拓扑绝缘体中的位错态

Dislocation defect states in acoustic quadrupole topological insulators

四极子拓扑绝缘体是人们提出的第一类高阶拓扑绝缘体,它具有量子化的四极矩而偶极矩为零.四极子拓扑绝缘体拓宽了传统的体-边对应关系,从而观察到了更低维度的拓扑边界态.最近,由局域在位错附近的拓扑缺陷态主导的体-位错对应关系引起了许多研究者的关注,其将晶格倒易空间的拓扑结构与位错态的出现联系起来.本文研究了声学四极子拓扑绝缘体中的位错态.在具有非平庸相的声学四极子拓扑绝缘体中嵌入部分具有平庸相的晶格,此时在由两种具有不同拓扑相晶格形成边界的角落处就会产生可以用1/2量化分数电荷表征的位错态.通过在系统内部引入缺陷,验证了此拓扑位错态的鲁棒性.此外,还证明了通过运用不同嵌入晶格的方式可以随意设计位错态的位置.本工作中研究的拓扑位错态拓宽了人工结构中高阶拓扑物态的种类,并为高阶拓扑绝缘体在声学中的应用(如声传感和高性能能量收集)提供了新的思路.

Quadrupole topological insulator(QTI)is the first proposed higher-order topological phase of matter with quantized quadrupole moment but zero dipole moment.The QTI has expanded widely the traditional bulkboundary correspondence,thereby the lower-dimensional topological boundary state can be observed.The recent interest has turned to the bulk-dislocation correspondence,which dominates the topological states localized to disclinations,and links the reciprocal-space topology of lattices with the appearance of dislocation states.Recently,many research groups have turned the studies of dislocation defects to classical wave systems.In these researches,the method of inducing dislocation defects is to remove a portion of the lattices of topological insulator and then rearrange the remaining lattices of the topological insulator.Through such a method,the micro structure of the lattices is changed,but it is difficult to realize in the actual operation.In this work,we study the dislocation defect states in acoustic QTIs.The acoustic QTI is designed by reversing the magnitude of the intracellular and extracellular coupling in the system,and the bulk energy bands and topological corner states are studied.Subsequently,by introducing partial trivial lattices into acoustic QTI structure,the dislocation bound states are generated in the corner formed by two different topological phases,which can be characterized by a 1/2 quantized fractional charge.The robustness of the topological dislocation states is verified by introducing the imperfection inside the system.Further,it is demonstrated that the dislocation positions can be designed at will.Without changing the microstructure of the lattice,we successfully modulate the line dislocation states and bulk dislocation states.The topological dislocation states studied in this work broaden the types of higher-order topological states in artificial structures,and provide new insights into the acoustic applications of higher-order topological insulators,such as sensing and high-performance energy harvesting.